Russian President Vladimir Putin has signed an order recognizing Ukraine's Crimea region as a sovereign and independent country.
Russian news agencies quoted the Kremlin press service as saying Putin signed the order on March 17.
The move comes after Crimea's regional parliament declared independence from Ukraine and formally applied for membership in the Russian Federation.
On March 16, pro-Russian authorities in Crimea held a referendum calling for the region to be annexed by Russia.
Putin says the referendum is legal. Russian lawmakers have drafted legislation to prepare for the annexation of Crimea under Russian constitutional law.
The United States and the European Union have refused to recognize the referendum results, saying the vote was illegal under Ukrainian and international law, and have imposed sanctions against Russian officials and pro-Russian Ukrainians.
President Barack Obama said the U.S. sanctions targeted 11 individuals, seven Russians and four Ukrainians, responsible for "undermining the sovereignty of Ukraine" and violating its territorial integrity.
Obama said any moves by Russia to annex Crimea will not be recognized by the international community. Obama also threatened additional measures if the Kremlin made "further provocations" in Ukraine.
"Now, I believe there is still a path to resolve this situation diplomatically, in a way that it addresses the interest of both Russia and Ukraine," Obama said.
"That includes Russia pulling its forces in Crimea back to their bases, supporting the deployment of additional international monitors in Ukraine, and engaging in dialogue with the Ukrainian government, which has indicated its openness to pursuing constitutional reform as they move forward towards elections this spring."
The U.S. sanctions list includes Russian Deputy Prime Minister Dmitry Rogozin; the head of the Federation Council upper house of parliament, Valentina Matviyenko; and two of President Vladimir Putin's aides, Vladislav Surkov and Sergei Glazyev.
It also includes State Duma lower-house Deputies Leonid Slutsky and Yelena Mizulina, and Federation Council member Andrei Klishas.
Ukrainians on the U.S. sanctions list include ousted President Viktor Yanukovych, the head of the pro-Russian Ukrainian Choice political organization, Viktor Medvedchuk; and two pro-Russian Crimean political leaders -- Sergei Aksyonov, who claims to be Crimean prime minister, and Vladimir Konstantinov, the speaker of Crimea's parliament.
White House spokesman Jay Carney did not rule out that Washington could eventually target Putin with sanctions, or provide U.S. military assistance to Ukraine's new authorities. But he said Washington's focus "continues to be on supporting economic and diplomatic measures to de-escalate the situation, not escalate it."
Earlier, the European Union said it would sign with Ukraine's new authorities the political provisions of an Association Agreement on March 21 -- the same agreement Yanukovych rejected in November, igniting the protests that led to his ouster.
The EU also announced travel bans and asset freezes against 21 pro-Russian Ukrainians and Russian officials.
They include Crimean pro-Russian leaders Aksyonov and Konstantinov; Ukrainian naval commander Deniz Berezovskiy, who has sworn an oath to Crimea's breakaway armed forces; and Russian lawmaker Sergei Mironov, who initiated a State Duma bill allowing Crimea's possible annexation.
British Foreign Secretary William Hague said sanctions could be expanded later.
"This is not a list that is set in stone for the future," he said. "It is possible to add other people in the future, depending on how Russia reacts to the referendum in Crimea, which has been a mockery of any real democracy."
EU foreign-policy chief Catherine Ashton said Brussels cannot recognize the outcome of an illegal referendum conducted where the Russian military has deployed.
"We want to underline very clearly that there is still time to avoid a negative spiral and to reverse current developments; and we call on the Russian leadership not to take steps to annex Crimea and instead to take steps to de-escalate this crisis," she said.
NATO also warned Russia against taking any steps to annex Crimea. The alliance called the March 16 referendum in Crimea on joining Russia "both illegal and illegitimate."
The NATO statement said the conditions under which the vote was held, including Russian military intervention as well as restrictions and manipulation of the media, "deprived the vote of any credibility."
It said "the so-called referendum undermines efforts to find a political solution" to the Ukrainian crisis. It urged Russia to deescalate the situation, including by ceasing all military activities against Ukraine.
The republican assembly in Crimea earlier in the day applied to secede from Ukraine and join the Russian Federation after a March 16 referendum, conducted with heavily armed Russian troops and self-styled "self-defense" forces patrolling the streets in Crimea, suggested nearly 97 percent support for the move.
German Chancellor Angela Merkel said she believed Russia has isolated itself in its recognition of the "so-called referendum."
"Russia is isolated to a large degree in its recognition of this so-called referendum," German government spokesman Steffen Seibert said.
"In the UN Security Council, there was a resolution which condemned the fact that this referendum goes against international law and is unconstitutional, with 13 countries in favor of it, China abstaining, and Russia using its power of veto. The chancellor once again communicated yesterday by telephone this clear position with President Putin."
Crimean lawmakers on March 17 also declared a series of measures aimed at propping up the region. They announced that all Ukrainian state property would become the property of the Crimean Republic. Energy companies Chornomornaftohaz and Ukrtransgaz will be "nationalized."
The Russian ruble was introduced as a second official currency alongside the Ukrainian hryvnya, with the hryvnya to be phased out by 2016.
The setting up of a central bank with Russian funding was announced. Crimea's 2014 budget was revised and would include Russian aid worth more than $409 billion.
The parliament speaker said Ukrainian military units in the region would be disbanded.
Ukraine's parliament, meanwhile, on March 17 endorsed a presidential decree to carry out a partial mobilization involving 40,000 reservists.
Ukraine's interim Foreign Minister Andriy Deshchytsya met with NATO Secretary-General Anders Fogh Rasmussen in Brussels to ask for "more technical military equipment."
NATO said in a statement the alliance was determined to boost cooperation, including "increased ties with Ukraine's political and military leadership, strengthening efforts to build the capacity of the Ukrainian military, and more joint training and exercises."
Ukraine has also recalled its ambassador to Russia for consultations. The Ukrainian Foreign Ministry announced that Ambassador Volodymyr Yelchenko was being called back to Kyiv.
With reporting by RFE/RL Brussels correspondent Rikard Jozwiak, Reuters, AFP, AP, and Interfax